B737 CREW FOLLOW WRONG ACFT ON A VISUAL APCH INTO LAX.

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WE WERE IN A R DOWNWIND PATTERN APPROX 7 MI E OF SMO VOR FOR AN INTENDED LNDG AT LAX ARPT ON RWY 24R. APCH CTL HAD INFORMED US THAT A B-777 WOULD BE PRECEDING US TO THE RWY. AT APPROX 10 MI E OF THE FIELD; APCH CTL CALLED OUT TFC AT OUR 4 O'CLOCK POS; OVER THE HOLLYWOOD PARK AREA. WE ACKNOWLEDGED THE B-777 AND THE RWY IN SIGHT AND WERE ISSUED THE VISUAL APCH CLRNC TO FOLLOW THAT ACFT TO RWY 24R. NO OTHER TFC WAS ISSUED TO US FOR ADVISORY. I STARTED A BASE TURN THAT WOULD ANGLE MORE DIRECTLY TO THE FIELD IN ORDER TO CUT DISTANCE BTWN US AND THE B-777. THE HEADING I CHOSE WAS APPROX 200 DEGS FOR THE INTERCEPT OF THE RWY 24R LOC. BOTH THE CAPT AND I HAD PREVIOUSLY TUNED IN OUR RESPECTIVE RECEIVERS. WHILE STARTING THIS TURN; WE WERE ASKED TO CHK IN WITH TWR; ON FREQ 133.9. WHILE CHANGING FREQ; I TOOK MY EYES OFF THE B-777 AND CALLED FOR FLAPS 5 DEGS WHILE COORDINATING THE TURN OF THE ACFT. TWR ACKNOWLEDGED THE CHK IN AND SAID WE WERE #2 BEHIND THAT B-777 ON A 1 MI FINAL FOR RWY 24R. BOTH THE CAPT AND I LOOKED UP AND SAW AT OUR 12 O'CLOCK POS AN ACFT 'LIKE' THE B-777. I WAS SOMEWHAT SURPRISED THAT IT WAS AS CLOSE AS IT WAS FOR I HAD ALREADY DETERMINED THE NEED FOR A TURN MORE DIRECT TO THE FIELD TO CLOSE THE GAP. I QUESTIONED THE CAPT IF THIS ACFT IN FRONT OF US WAS THE ONE WE WERE TO FOLLOW. HE THOUGHT IT WAS AND SAID THAT WE WERE AT ABOUT 4 MI FROM IT AND CLOSING. I DISCONNECTED THE AUTOPLT AND SLOWED THE ACFT WHILE CALLING FOR 'LNDG GEAR DOWN; FLAPS 15 DEGS; FINAL APCH CHKLIST.' WHILE COMPENSATING FOR SPACING ON THAT ACFT AND COMPLETING THE FINAL APCH CHKLIST; WE FLEW THROUGH THE LOC FOR RWY 24R. AND WE DID SO WITHOUT EITHER OF US NOTICING IT. IT WASN'T UNTIL WE ALMOST LINED UP WITH RWY 24R THAT I OBSERVED THE FULL DEFLECTION OF MY RECEIVER FOR THE LOC. I IMMEDIATELY STARTED A CORRECTION BACK TO THE PROPER RWY WHEN TWR SAID WE HAD LINED UP ON THE WRONG RWY AND ISSUED THE CORRECT LOC FREQ TO TUNE TO. WE APOLOGIZED FOR OUR ERROR AND CONTINUED BACK TO THE CORRECT RWY WHILE FINISHING OUR CONFIGN FOR LNDG. WE MADE A NORMAL LNDG ON RWY 24R WITH NO FURTHER INCIDENT. CAUSES: NO REF WAS MADE BY APCH CTL FOR ANOTHER ACFT TO THE S COMPLEX TO WATCH FOR. I TURNED ALL MY ATTN TO THE SUPPOSED ACFT WE WERE TO FOLLOW WITHOUT XCHKING THE LOC COURSE FOR PROPER LINE UP. IT WAS A VISUALLY CLR DAY AT 6 MI. THE RWYS WERE SLIGHTLY OBSCURED AND LENT ITSELF EASILY TO MISIDENT FOR THE PROPER COMPLEX. PREVENTION: KEEP THE AUTOPLT ENGAGED WITH THE LOC CAPTURE SELECTED IN ORDER TO HAVE A BACK UP. THE RWY I WAS CLRED TO IS THE PRIMARY CONCERN AND I SHOULD LINE UP ACCORDINGLY. HAD I DONE SO; I WOULD HAVE NOTICED THAT THAT ACFT WAS GOING TO A DIFFERENT COMPLEX THAN OURS. ALWAYS DOUBLE CHK ONESELF WHEN THERE IS A QUESTION IN THE MIND ABOUT THE RELATIVE POS OF THE ACFT WE ARE ASSIGNED TO FOLLOW. SUPPLEMENTAL INFO FROM ACN 582889: WE BOTH HAD ILS RWY 24R DIALED UP AND COURSE SET; BUT WERE HAVING DIFFICULTY KEEPING THE B-777 IN SIGHT. (VISIBILITY LOOKED LIKE 4-6 MI.) I WAS HEADS DOWN FOR A MOMENT WATCHING THE TCASII SCOPE FOR SEPARATION WHEN THE FO EXPRESSED SURPRISE AND ALARM. AS I LOOKED UP; TWR CALLED US AND TOLD US WE WERE LINED UP FOR RWY 25L. WE FOLLOWED A WRONG ACFT APPARENTLY TO RWY 25L IN THE REDUCED VISIBILITY. WE CORRECTED AND LANDED UNEVENTFULLY.